From 7dfc866a579ce1f564b67a78cc44bb0c6099d783 Mon Sep 17 00:00:00 2001 From: Julie Hogan Date: Thu, 11 Jan 2024 21:32:03 +0000 Subject: [PATCH 1/7] backgrounds page; MathJax; tweak nav --- docs/analysis/backgrounds.md | 143 ++++++++++++++++++ docs/analysis/backgrounds/qcdestimation.md | 4 - docs/analysis/backgrounds/techniques.md | 4 - docs/analysis/{luminosity => }/lumi.md | 0 docs/analysis/selection/validatedRuns.md | 2 +- docs/analysis/systematics/objectsuncertain.md | 4 - docs/images/ABCD.png | Bin 0 -> 49497 bytes docs/images/ABCDext.png | Bin 0 -> 64131 bytes docs/javascripts/mathjax.js | 16 ++ mkdocs.yml | 17 ++- 10 files changed, 170 insertions(+), 20 deletions(-) create mode 100644 docs/analysis/backgrounds.md delete mode 100644 docs/analysis/backgrounds/qcdestimation.md delete mode 100644 docs/analysis/backgrounds/techniques.md rename docs/analysis/{luminosity => }/lumi.md (100%) delete mode 100644 docs/analysis/systematics/objectsuncertain.md create mode 100644 docs/images/ABCD.png create mode 100644 docs/images/ABCDext.png create mode 100644 docs/javascripts/mathjax.js diff --git a/docs/analysis/backgrounds.md b/docs/analysis/backgrounds.md new file mode 100644 index 00000000..ffbd035b --- /dev/null +++ b/docs/analysis/backgrounds.md @@ -0,0 +1,143 @@ +# Background Modelling Techniques + +!!! Warning + This page is under construction + +Accurate modeling of SM background processes is essential to most searches and measurements in high energy physics. +The dominant background processes depend strongly on the selected objects, particularly leptons, missing +transverse momentum, and b quark jets or jets from boosted particles. Background estimation strategies +are always tailored to an individual analysis, typically as a variation of one or more of the following +common methods. + +## Simulation + +Many SM processes are simulated at NLO, which provides a strong basis for background +estimation. For processes such as W/Z+jets production that are often simulated at LO, *k*-factor +calculations allows one to weight simulated events to reproduce predictions of distributions at NLO. +In final states with charged leptons, for which QCD multijet production is unlikely to be a significant background, simulation is a common choice. +Additionally, the majority of searches utilize simulation to model the signal process under consideration. + +Simulated events are weighted so that the efficiencies of certain selections +in simulation match those observed in data. These corrections are referred to as ``scale factors''. +Common scale factors in searches at the CMS experiment correct +for differences in : + +- the number of pileup interactions +- the efficiencies of trigger selections +- the efficiencies of charged lepton identification and isolation selection criteria +- the efficiencies of various jet identification selection criteria, such as heavy-flavor tagging. + +A detailed set of [corrections for the jet energy scale and resolution](systematics/objectsuncertain/jetmetuncertain.md) are computed for simulated events so that the +response of the jet reconstruction algorithms is consistent between observed data and simulation. Searches may also develop +correction formulas to correct for observed mismodeling of data by simulation in certain distributions of interest. +A common correction of this type is to reweight the reconstructed top quark \pt spectrum, since the NLO top quark pair simulations +tend to overpredict the rate of high-\pt top quark pairs. Each correction applied to simulation carries an uncertainty +that should be taken into account in the statistical methods of signal extraction. + +## Tight / loose or "Matrix" methods + +Searches that select multiple charged leptons often have considerable background +from events in which *nonprompt* leptons are selected. Nonprompt leptons are usually charged leptons that arise from +sources other than the hard scatter or decays of massive particles produced in the hard scatter. + +One method to estimate contributions from these events is to measure how often known prompt leptons, typically from the +decay of Z bosons, and known nonprompt leptons, typically from a sample of QCD multijet events, pass a certain set of +lepton selection criteria. A Z boson sample is created in data by selecting events with two same-flavor opposite-sign +leptons whose mass lies very close to the Z boson mass. One lepton, known as the *tag*, is selected using very high-purity +selection criteria, giving confidence that the other *probe* lepton is indeed a prompt lepton. The efficiency for the +probe lepton to pass any criteria of interest can then be measured in this sample (learn more about this calculation +on the [tag and probe page](selection/idefficiencystudy/tagandprobe.md)). In the context of this background +estimation method, the efficiency of the analysis selection criteria is referred to as the *prompt rate*, $p$. + +A QCD multijet sample can be created by selecting events that pass a low-momentum, low-purity, single-lepton trigger, but otherwise +exhibit no strong signs of the lepton arising from a SM boson decay. The rate at which these leptons pass the analysis selection +criteria can be measured, and is referred to as the *nonprompt* rate (or colloquially, *fake* rate), $f$. Both of these rates +describe how often either prompt or nonprompt leptons that pass some baseline *loose* selection also pass the *tight* +selection criteria used in the analysis. + +For searches that probe final states with two charged leptons, the probabilities for any prompt or nonprompt lepton to enter the sample must be considered +together to develop a background distribution. +The number of events with leptons passing the tight and/or loose criteria may be observed, in particular the number of events with two tight leptons, \(N_{tt}\); one tight and one loose lepton, \(N_{tl}\); and two loose leptons, \(N_{ll}\). +The prompt and nonprompt rates may then be used to convert those observations into numbers of events with two prompt leptons, \(N_{pp}\); one prompt and one nonprompt lepton, \(N_{pf}\); and two nonprompt leptons, \(N_{ff}\). + +\[ +\begin{pmatrix} + N_{tt} \\ + N_{tl} \\ + N_{ll} +\end{pmatrix} = \left( \begin{array}{ccc} + p^2 & pf & f^2 \\ + 2p(1-p) & f(1-p) + p(1-f) & 2f(1-f) \\ + (1-p)^2 & (1-p)(1-f) & (1-f)^2 +\end{array} \right) +\begin{pmatrix} + N_{pp}\\ + N_{pf}\\ + N_{ff} +\end{pmatrix} +\] + +A matrix inversion provides formulas to calculate \(N_{pf}\) and \(N_{ff}\) from the observed number of events with leptons of +varying quality. For a search selecting two tight leptons, the background from events with nonprompt leptons will be given +by \(N_{\mathrm{bkg}} = pfN_{pf} + f^2N_{ff}\). This method can be extended to searches targeting final states more than two charged leptons by expanding the probability matrix. + +A good reference for this method, built on earlier uses within CMS, is the [2022 doctoral thesis of Wing Yan Wong](http://cds.cern.ch/record/2808538). + +## Transfer factors + +In many searches, one important selection criterion is the primary dividing line between +a background-dominated control region (CR) and a region with good signal sensitivity, called the signal region (SR). +A *transfer factor* or *transfer function* +that describes the efficiency of this principle selection criteria can be derived and applied to the observed data in the +CR in order to estimate the background present in the SR. + +### Alpha-ratio method +The transfer function can be computed in multiple ways. Some searches use simulation for this purpose, in which +case the method is often called the *alpha-ratio method*. The number of background events in the SR, \(N_{\mathrm{SR}}^{bkg}\), is calculated +as: + +\[ +N_{\mathrm{SR}}^{bkg} = N_\mathrm{CR}^{data} \times \frac{N_{\mathrm{SR}}^{sim}}{N_{\mathrm{CR}}^{sim}}, +\] + +where \(N_\mathrm{CR}^{data}\) is the number of observed collision events in the CR, \(N_{\mathrm{SR}}^{sim}\) is the number of simulated events in the SR, +and \(N_{\mathrm{CR}}^{sim}\) is the number of simulated events in the CR. +The transfer factor from simulation can be computed in any bin of an observable, so the shape as well as the rate of +background in the SR may be obtained. + + +### ABCD method +Other searches measure transfer factors using observed data in selection regions that are distinct from the primary SR and CR, +in which case the method might be referred to as the **ABCD method**. This method is particularly popular for dealing with multijet +backgrounds that are not typically modelled well by simulation. + +Four selection regions in the observed data are involved, +formed by events either passing or failing either of two selection criteria, as shown in the graphic below. The +number of background events in the SR (region C), \(N_\mathrm{C}\), is calculated from observations in regions A, B, and D as +\(N_\mathrm{D} \times (N_\mathrm{B} / N_\mathrm{A})\). This method may also be used in any bin of an observable to obtain a shape-based prediction for the background. +In general, the ABCD method requires that the selection criteria are statistically independent in order to produce unbiased predictions. + +![](../images/ABCD.png) + +If some background sources are well-modelled by +simulation, these contributions may be subtracted from the observed data in each region before computing or applying the transfer function. +More than four regions can be used to incorporate a method for validation into the procedure, as shown in the second graphic. +The number of background events in the validation region X is estimated from the observations in regions A, D, and Y as \(N_\mathrm{D} \times (N_\mathrm{Y} / N_\mathrm{A})\), and if region X has a suitably low rate of +expected signal events the observed data in this region could be compared to the background prediction, to test the validity +of the prediction method. + +![](../images/ABCDext.png) + +## Sideband fits + +In many searches, the observable most sensitive to the signal is a reconstructed mass +or jet mass distribution, in which the signal is expected to be resonant while the dominant background +processes are non-resonant. The shape of the background distribution may then be predicted by fitting a smooth +functional form to the observed data on either side of the region in which the signal distribution is expected to peak. This method +may be used in multiple dimensions for signals that feature more than one resonance. + +When multiple +functional forms offer adequate fits to the observed data, an F-statistic may be used to compare the residual sums of +squares for two formulas and determine whether a formula with more parameters provides a significantly better +fit than an alternate formula with fewer parameters (known as the Fischer \(\mathcal{F}\)-test). + diff --git a/docs/analysis/backgrounds/qcdestimation.md b/docs/analysis/backgrounds/qcdestimation.md deleted file mode 100644 index 07abd139..00000000 --- a/docs/analysis/backgrounds/qcdestimation.md +++ /dev/null @@ -1,4 +0,0 @@ -# QCD Estimation - -!!! Warning - This page is under construction diff --git a/docs/analysis/backgrounds/techniques.md b/docs/analysis/backgrounds/techniques.md deleted file mode 100644 index 0d69a731..00000000 --- a/docs/analysis/backgrounds/techniques.md +++ /dev/null @@ -1,4 +0,0 @@ -# Techniques - -!!! Warning - This page is under construction diff --git a/docs/analysis/luminosity/lumi.md b/docs/analysis/lumi.md similarity index 100% rename from docs/analysis/luminosity/lumi.md rename to docs/analysis/lumi.md diff --git a/docs/analysis/selection/validatedRuns.md b/docs/analysis/selection/validatedRuns.md index ca7722a7..0276ba88 100644 --- a/docs/analysis/selection/validatedRuns.md +++ b/docs/analysis/selection/validatedRuns.md @@ -41,4 +41,4 @@ and by adding these two lines after the `process.source` input file definition: process.source.lumisToProcess.extend(myLumis) ``` -This list should also be used as an input to the [luminosity calculation](../luminosity/lumi.md). +This list should also be used as an input to the [luminosity calculation](../lumi.md). diff --git a/docs/analysis/systematics/objectsuncertain.md b/docs/analysis/systematics/objectsuncertain.md deleted file mode 100644 index 86a2caae..00000000 --- a/docs/analysis/systematics/objectsuncertain.md +++ /dev/null @@ -1,4 +0,0 @@ -# Object Uncertainty - -!!! 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Background estimation strategies are always tailored to an individual analysis, typically as a variation of one or more of the following -common methods. +common methods. ## Simulation @@ -18,7 +18,7 @@ In final states with charged leptons, for which QCD multijet production is unlik Additionally, the majority of searches utilize simulation to model the signal process under consideration. Simulated events are weighted so that the efficiencies of certain selections -in simulation match those observed in data. These corrections are referred to as ``scale factors''. +in simulation match those observed in data. These corrections are referred to as ``scale factors''. Common scale factors in searches at the CMS experiment correct for differences in : @@ -27,9 +27,9 @@ for differences in : - the efficiencies of charged lepton identification and isolation selection criteria - the efficiencies of various jet identification selection criteria, such as heavy-flavor tagging. -A detailed set of [corrections for the jet energy scale and resolution](systematics/objectsuncertain/jetmetuncertain.md) are computed for simulated events so that the +A detailed set of [corrections for the jet energy scale and resolution](systematics/objectsuncertain/jetmetuncertain.md) are computed for simulated events so that the response of the jet reconstruction algorithms is consistent between observed data and simulation. Searches may also develop -correction formulas to correct for observed mismodeling of data by simulation in certain distributions of interest. +correction formulas to correct for observed mismodeling of data by simulation in certain distributions of interest. A common correction of this type is to reweight the reconstructed top quark \pt spectrum, since the NLO top quark pair simulations tend to overpredict the rate of high-\pt top quark pairs. Each correction applied to simulation carries an uncertainty that should be taken into account in the statistical methods of signal extraction. @@ -37,26 +37,26 @@ that should be taken into account in the statistical methods of signal extractio ## Tight / loose or "Matrix" methods Searches that select multiple charged leptons often have considerable background -from events in which *nonprompt* leptons are selected. Nonprompt leptons are usually charged leptons that arise from +from events in which *nonprompt* leptons are selected. Nonprompt leptons are usually charged leptons that arise from sources other than the hard scatter or decays of massive particles produced in the hard scatter. -One method to estimate contributions from these events is to measure how often known prompt leptons, typically from the -decay of Z bosons, and known nonprompt leptons, typically from a sample of QCD multijet events, pass a certain set of +One method to estimate contributions from these events is to measure how often known prompt leptons, typically from the +decay of Z bosons, and known nonprompt leptons, typically from a sample of QCD multijet events, pass a certain set of lepton selection criteria. A Z boson sample is created in data by selecting events with two same-flavor opposite-sign leptons whose mass lies very close to the Z boson mass. One lepton, known as the *tag*, is selected using very high-purity selection criteria, giving confidence that the other *probe* lepton is indeed a prompt lepton. The efficiency for the probe lepton to pass any criteria of interest can then be measured in this sample (learn more about this calculation on the [tag and probe page](selection/idefficiencystudy/tagandprobe.md)). In the context of this background -estimation method, the efficiency of the analysis selection criteria is referred to as the *prompt rate*, $p$. +estimation method, the efficiency of the analysis selection criteria is referred to as the *prompt rate*, $p$. -A QCD multijet sample can be created by selecting events that pass a low-momentum, low-purity, single-lepton trigger, but otherwise -exhibit no strong signs of the lepton arising from a SM boson decay. The rate at which these leptons pass the analysis selection -criteria can be measured, and is referred to as the *nonprompt* rate (or colloquially, *fake* rate), $f$. Both of these rates +A QCD multijet sample can be created by selecting events that pass a low-momentum, low-purity, single-lepton trigger, but otherwise +exhibit no strong signs of the lepton arising from a SM boson decay. The rate at which these leptons pass the analysis selection +criteria can be measured, and is referred to as the *nonprompt* rate (or colloquially, *fake* rate), $f$. Both of these rates describe how often either prompt or nonprompt leptons that pass some baseline *loose* selection also pass the *tight* selection criteria used in the analysis. For searches that probe final states with two charged leptons, the probabilities for any prompt or nonprompt lepton to enter the sample must be considered -together to develop a background distribution. +together to develop a background distribution. The number of events with leptons passing the tight and/or loose criteria may be observed, in particular the number of events with two tight leptons, \(N_{tt}\); one tight and one loose lepton, \(N_{tl}\); and two loose leptons, \(N_{ll}\). The prompt and nonprompt rates may then be used to convert those observations into numbers of events with two prompt leptons, \(N_{pp}\); one prompt and one nonprompt lepton, \(N_{pf}\); and two nonprompt leptons, \(N_{ff}\). @@ -68,7 +68,7 @@ The prompt and nonprompt rates may then be used to convert those observations in \end{pmatrix} = \left( \begin{array}{ccc} p^2 & pf & f^2 \\ 2p(1-p) & f(1-p) + p(1-f) & 2f(1-f) \\ - (1-p)^2 & (1-p)(1-f) & (1-f)^2 + (1-p)^2 & (1-p)(1-f) & (1-f)^2 \end{array} \right) \begin{pmatrix} N_{pp}\\ @@ -83,15 +83,16 @@ by \(N_{\mathrm{bkg}} = pfN_{pf} + f^2N_{ff}\). This method can be extended to s A good reference for this method, built on earlier uses within CMS, is the [2022 doctoral thesis of Wing Yan Wong](http://cds.cern.ch/record/2808538). -## Transfer factors +## Transfer factors In many searches, one important selection criterion is the primary dividing line between -a background-dominated control region (CR) and a region with good signal sensitivity, called the signal region (SR). +a background-dominated control region (CR) and a region with good signal sensitivity, called the signal region (SR). A *transfer factor* or *transfer function* -that describes the efficiency of this principle selection criteria can be derived and applied to the observed data in the -CR in order to estimate the background present in the SR. +that describes the efficiency of this principle selection criteria can be derived and applied to the observed data in the +CR in order to estimate the background present in the SR. ### Alpha-ratio method + The transfer function can be computed in multiple ways. Some searches use simulation for this purpose, in which case the method is often called the *alpha-ratio method*. The number of background events in the SR, \(N_{\mathrm{SR}}^{bkg}\), is calculated as: @@ -100,44 +101,42 @@ as: N_{\mathrm{SR}}^{bkg} = N_\mathrm{CR}^{data} \times \frac{N_{\mathrm{SR}}^{sim}}{N_{\mathrm{CR}}^{sim}}, \] -where \(N_\mathrm{CR}^{data}\) is the number of observed collision events in the CR, \(N_{\mathrm{SR}}^{sim}\) is the number of simulated events in the SR, +where \(N_\mathrm{CR}^{data}\) is the number of observed collision events in the CR, \(N_{\mathrm{SR}}^{sim}\) is the number of simulated events in the SR, and \(N_{\mathrm{CR}}^{sim}\) is the number of simulated events in the CR. -The transfer factor from simulation can be computed in any bin of an observable, so the shape as well as the rate of +The transfer factor from simulation can be computed in any bin of an observable, so the shape as well as the rate of background in the SR may be obtained. - ### ABCD method -Other searches measure transfer factors using observed data in selection regions that are distinct from the primary SR and CR, + +Other searches measure transfer factors using observed data in selection regions that are distinct from the primary SR and CR, in which case the method might be referred to as the **ABCD method**. This method is particularly popular for dealing with multijet backgrounds that are not typically modelled well by simulation. -Four selection regions in the observed data are involved, +Four selection regions in the observed data are involved, formed by events either passing or failing either of two selection criteria, as shown in the graphic below. The -number of background events in the SR (region C), \(N_\mathrm{C}\), is calculated from observations in regions A, B, and D as +number of background events in the SR (region C), \(N_\mathrm{C}\), is calculated from observations in regions A, B, and D as \(N_\mathrm{D} \times (N_\mathrm{B} / N_\mathrm{A})\). This method may also be used in any bin of an observable to obtain a shape-based prediction for the background. In general, the ABCD method requires that the selection criteria are statistically independent in order to produce unbiased predictions. -![](../images/ABCD.png) +![Demonstration of the ABCD method](../images/ABCD.png) -If some background sources are well-modelled by +If some background sources are well-modelled by simulation, these contributions may be subtracted from the observed data in each region before computing or applying the transfer function. More than four regions can be used to incorporate a method for validation into the procedure, as shown in the second graphic. -The number of background events in the validation region X is estimated from the observations in regions A, D, and Y as \(N_\mathrm{D} \times (N_\mathrm{Y} / N_\mathrm{A})\), and if region X has a suitably low rate of +The number of background events in the validation region X is estimated from the observations in regions A, D, and Y as \(N_\mathrm{D} \times (N_\mathrm{Y} / N_\mathrm{A})\), and if region X has a suitably low rate of expected signal events the observed data in this region could be compared to the background prediction, to test the validity -of the prediction method. +of the prediction method. -![](../images/ABCDext.png) +![Demonstration of ABCD method with a validation region](../images/ABCDext.png) ## Sideband fits In many searches, the observable most sensitive to the signal is a reconstructed mass or jet mass distribution, in which the signal is expected to be resonant while the dominant background -processes are non-resonant. The shape of the background distribution may then be predicted by fitting a smooth +processes are non-resonant. The shape of the background distribution may then be predicted by fitting a smooth functional form to the observed data on either side of the region in which the signal distribution is expected to peak. This method may be used in multiple dimensions for signals that feature more than one resonance. -When multiple -functional forms offer adequate fits to the observed data, an F-statistic may be used to compare the residual sums of +When multiple functional forms offer adequate fits to the observed data, an F-statistic may be used to compare the residual sums of squares for two formulas and determine whether a formula with more parameters provides a significantly better -fit than an alternate formula with fewer parameters (known as the Fischer \(\mathcal{F}\)-test). - +fit than an alternate formula with fewer parameters (known as the Fischer \(\mathcal{F}\)-test). \ No newline at end of file From c12cc8d04c349e084b7dae31e0b12ca8b75d3c8e Mon Sep 17 00:00:00 2001 From: Julie Hogan Date: Thu, 11 Jan 2024 21:47:17 +0000 Subject: [PATCH 3/7] backgrounds.md learning rules... --- docs/analysis/backgrounds.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/analysis/backgrounds.md b/docs/analysis/backgrounds.md index 1b2741a9..69a581bc 100644 --- a/docs/analysis/backgrounds.md +++ b/docs/analysis/backgrounds.md @@ -139,4 +139,4 @@ may be used in multiple dimensions for signals that feature more than one resona When multiple functional forms offer adequate fits to the observed data, an F-statistic may be used to compare the residual sums of squares for two formulas and determine whether a formula with more parameters provides a significantly better -fit than an alternate formula with fewer parameters (known as the Fischer \(\mathcal{F}\)-test). \ No newline at end of file +fit than an alternate formula with fewer parameters (known as the Fischer \(\mathcal{F}\)-test). From 581cb1813cbc2d45f8aafb866754f067b50eae3f Mon Sep 17 00:00:00 2001 From: Julie Hogan Date: Fri, 12 Jan 2024 17:22:03 +0000 Subject: [PATCH 4/7] statistics page, tweak nav --- docs/analysis/interpretation/stats.md | 4 -- docs/analysis/stats.md | 56 +++++++++++++++++++++++++++ mkdocs.yml | 4 +- 3 files changed, 57 insertions(+), 7 deletions(-) delete mode 100644 docs/analysis/interpretation/stats.md create mode 100644 docs/analysis/stats.md diff --git a/docs/analysis/interpretation/stats.md b/docs/analysis/interpretation/stats.md deleted file mode 100644 index 5ba770ed..00000000 --- a/docs/analysis/interpretation/stats.md +++ /dev/null @@ -1,4 +0,0 @@ -# Statistics - -!!! Warning - This page is under construction diff --git a/docs/analysis/stats.md b/docs/analysis/stats.md new file mode 100644 index 00000000..9d789ee5 --- /dev/null +++ b/docs/analysis/stats.md @@ -0,0 +1,56 @@ +# Statistics + +!!! Warning + This page is under construction + +## Overview of CMS techniques + +CMS searches typically determine an observable or set of observables that is used to measure the potential presence of +signal events. This can be any observable, preferably highlighting unique features of the signal process. +Signal extraction is based on maximum likelihood fits that compare ``data'' (either collision data or pseudodata +sampled from a test distribution) to the signal (\(s\)) and background (\(b\)) predictions, with signal scaled by some +unknown ratio \(\mu\). The likelihood is assumed to follow a Poisson distribution, and all predictions are subject to various +nuisance parameters, \(\theta\), that are given default values \(\tilde{\theta}\) and assigned probability density functions (\(p\)). +The likelihood function can be written as: + +\[ +\mathcal{L}(\mathrm{data}\vert \mu,\theta) = \mathrm{Poisson}(\mathrm{data}\vert \mu\cdot s(\theta) + b(\theta))\cdot p(\tilde{\theta}\vert\theta). +\] + +Systematic uncertainties are incorporated into the fit as nuisance parameters. Lognormal probability distributions are assigned +to uncertainties that affect only the normalization of a histogram or rate of a predicted event yield, and Gaussian probability +distributions are typically assigned to uncertainties provided as histograms that affect the shape of a distribution. +You can learn about several typical sources of uncertainty in CMS analyses in the [Systematics section](systematics/lumiuncertain.md) +of the Guide. + +Observed and expected limits on the signal ratio \(\mu\) are extracted by comparing the compatibility +of the observed data with a background-only (\(\mu = 0\)) hypothesis as well as with a signal+background hypothesis. +The most common statistical method within CMS is the **CLs** method ([Read, 2002](https://iopscience.iop.org/article/10.1088/0954-3899/28/10/313) and [Junk, 1999](https://www.sciencedirect.com/science/article/pii/S0168900299004982)), +which can be used to obtain a limit at the 95% confidence level using the profile likelihood test statistic +([Cowan, 2010](https://arxiv.org/abs/1007.1727)) with the asymptotic limit approximation. + +The ["Higgs Combine"](https://cms-analysis.github.io/HiggsAnalysis-CombinedLimit/) software framework used by +the CMS experiment to compute limits is built on the [RooFit](https://root.cern/manual/roofit/) and +[RooStats](https://root.cern/doc/master/group__Roostats.html) packages and implements statistical procedures developed +for combining ATLAS and CMS Higgs boson measurements. + +## Tutorials + +Many tutorials and lectures on statistical interpretation of LHC data are available online. Some selected highlights are listed here. + +- *Practical Statistics for LHC Physicists*, a set of three lectures by Prof. Harrison Prosper, 2015. Slides and videos are available for each lecture: + + * [Descriptive Statistics, Probability and Likelihood](https://indico.cern.ch/event/358542/) + * [Frequentist Inference](https://indico.cern.ch/event/358543/) + * [Bayesian Inference](https://indico.cern.ch/event/358544/) + +- Higgs Combine [tutorial on the main features of Combine](https://cms-analysis.github.io/HiggsAnalysis-CombinedLimit/part5/longexercise/). + + * [Solutions](https://cms-analysis.github.io/HiggsAnalysis-CombinedLimit/part5/longexerciseanswers/) are available + * Note: some links within this tutorial point to CMS internal resources. + +- Open Data Workshop [*Simplified Run 2 Analysis* lesson](https://cms-opendata-workshop.github.io/workshopwhepp-lesson-ttbarljetsanalysis/) + + * Lessons from the Open Data Workshop series use the docker container environment recommended for processing Open Data. + * The overall lesson offers tools for analysis of files in the NanoAOD or [PhysObjectExtractorTool](https://github.com/cms-opendata-analyses/PhysObjectExtractorTool) format. + * Specifically, the final page of the lesson (*5: Systematics and Statistics*) offers a python-based tool for performing statistical inference. diff --git a/mkdocs.yml b/mkdocs.yml index 073e74de..e7d02a04 100644 --- a/mkdocs.yml +++ b/mkdocs.yml @@ -75,9 +75,7 @@ nav: - 'Jet/MET uncertainties': analysis/systematics/objectsuncertain/jetmetuncertain.md - 'Tagging uncertainties': analysis/systematics/objectsuncertain/btaguncertain.md - 'Pileup Uncertainty': analysis/systematics/pileupuncertain.md - - 'Interpretation': - - 'Statistics': analysis/interpretation/stats.md - - 'Upper-limit Calculations': analysis/interpretation/limits.md + - 'Statistical Interpretation': analysis/stats.md - FAQ: faq.md - About: about.md From 28d44049ffaffbd377e953afac7115e59bf376ed Mon Sep 17 00:00:00 2001 From: Julie Hogan Date: Fri, 12 Jan 2024 17:28:04 +0000 Subject: [PATCH 5/7] stats: learning style rules --- docs/analysis/stats.md | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/docs/analysis/stats.md b/docs/analysis/stats.md index 9d789ee5..d1bb803c 100644 --- a/docs/analysis/stats.md +++ b/docs/analysis/stats.md @@ -36,21 +36,21 @@ for combining ATLAS and CMS Higgs boson measurements. ## Tutorials -Many tutorials and lectures on statistical interpretation of LHC data are available online. Some selected highlights are listed here. +Many tutorials and lectures on statistical interpretation of LHC data are available online. Some selected highlights are listed here. - *Practical Statistics for LHC Physicists*, a set of three lectures by Prof. Harrison Prosper, 2015. Slides and videos are available for each lecture: - * [Descriptive Statistics, Probability and Likelihood](https://indico.cern.ch/event/358542/) - * [Frequentist Inference](https://indico.cern.ch/event/358543/) - * [Bayesian Inference](https://indico.cern.ch/event/358544/) + - [Descriptive Statistics, Probability and Likelihood](https://indico.cern.ch/event/358542/) + - [Frequentist Inference](https://indico.cern.ch/event/358543/) + - [Bayesian Inference](https://indico.cern.ch/event/358544/) - Higgs Combine [tutorial on the main features of Combine](https://cms-analysis.github.io/HiggsAnalysis-CombinedLimit/part5/longexercise/). - * [Solutions](https://cms-analysis.github.io/HiggsAnalysis-CombinedLimit/part5/longexerciseanswers/) are available - * Note: some links within this tutorial point to CMS internal resources. + - [Solutions](https://cms-analysis.github.io/HiggsAnalysis-CombinedLimit/part5/longexerciseanswers/) are available + - Note: some links within this tutorial point to CMS internal resources. - Open Data Workshop [*Simplified Run 2 Analysis* lesson](https://cms-opendata-workshop.github.io/workshopwhepp-lesson-ttbarljetsanalysis/) - * Lessons from the Open Data Workshop series use the docker container environment recommended for processing Open Data. - * The overall lesson offers tools for analysis of files in the NanoAOD or [PhysObjectExtractorTool](https://github.com/cms-opendata-analyses/PhysObjectExtractorTool) format. - * Specifically, the final page of the lesson (*5: Systematics and Statistics*) offers a python-based tool for performing statistical inference. + - Lessons from the Open Data Workshop series use the docker container environment recommended for processing Open Data. + - The overall lesson offers tools for analysis of files in the NanoAOD or [PhysObjectExtractorTool](https://github.com/cms-opendata-analyses/PhysObjectExtractorTool) format. + - Specifically, the final page of the lesson (*5: Systematics and Statistics*) introduces the python-based tool [pyhf](https://pyhf.readthedocs.io/en/v0.7.6/) for performing statistical inference without any ROOT software. From f292e0a131ff5141cd02019e2a04530b97ca030f Mon Sep 17 00:00:00 2001 From: Julie Hogan Date: Fri, 12 Jan 2024 17:38:30 +0000 Subject: [PATCH 6/7] stats, typing a link manually --- docs/analysis/stats.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/analysis/stats.md b/docs/analysis/stats.md index d1bb803c..63f49971 100644 --- a/docs/analysis/stats.md +++ b/docs/analysis/stats.md @@ -29,7 +29,7 @@ The most common statistical method within CMS is the **CLs** method ([Read, 2002 which can be used to obtain a limit at the 95% confidence level using the profile likelihood test statistic ([Cowan, 2010](https://arxiv.org/abs/1007.1727)) with the asymptotic limit approximation. -The ["Higgs Combine"](https://cms-analysis.github.io/HiggsAnalysis-CombinedLimit/) software framework used by +The ["Higgs Combine"](https://cms-analysis.github.io/HiggsAnalysis-CombinedLimit) software framework used by the CMS experiment to compute limits is built on the [RooFit](https://root.cern/manual/roofit/) and [RooStats](https://root.cern/doc/master/group__Roostats.html) packages and implements statistical procedures developed for combining ATLAS and CMS Higgs boson measurements. From 25c8ff03b71636719514b6a0cf0cabe777933dfa Mon Sep 17 00:00:00 2001 From: Julie Hogan Date: Fri, 12 Jan 2024 14:34:51 -0600 Subject: [PATCH 7/7] stats new article links from awesome-bot tests --- docs/analysis/stats.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/analysis/stats.md b/docs/analysis/stats.md index 63f49971..8bf16248 100644 --- a/docs/analysis/stats.md +++ b/docs/analysis/stats.md @@ -25,7 +25,7 @@ of the Guide. Observed and expected limits on the signal ratio \(\mu\) are extracted by comparing the compatibility of the observed data with a background-only (\(\mu = 0\)) hypothesis as well as with a signal+background hypothesis. -The most common statistical method within CMS is the **CLs** method ([Read, 2002](https://iopscience.iop.org/article/10.1088/0954-3899/28/10/313) and [Junk, 1999](https://www.sciencedirect.com/science/article/pii/S0168900299004982)), +The most common statistical method within CMS is the **CLs** method ([Read, 2002](http://dx.doi.org/10.1088/0954-3899/28/10/313) and [Junk, 1999](https://www.arxiv.org/abs/hep-ex/9902006)), which can be used to obtain a limit at the 95% confidence level using the profile likelihood test statistic ([Cowan, 2010](https://arxiv.org/abs/1007.1727)) with the asymptotic limit approximation.